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Modeling the growth kinetics of a multi-component stoichiometric compound

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Abstract

The maximal entropy production principle was applied to model the growth kinetics of a multi-component stoichiometric compound. Compared with the solid-solution phase and the non-stoichiometric compound, the dissipation by the trans-interface diffusion makes the interface slow down by decreasing the effective interface mobility and does not result in solute trap** or disorder trap**. An application to the crystallization of a CuZr stoichiometric compound shows that the transition from the thermodynamic-controlled to the kinetic-controlled growth can be predicted.

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Notes

  1. For the solid-solution phase, \( \Updelta g \) can be divided into the driving free energy for the interface migration \( \Updelta g_{\text{C}} \) and the trans-interface diffusion \( \Updelta g_{\text{D}} \) by moving the tangent of the solid curve at \( C_{\text{S}} \) to \( C_{\text{L}}^{ *} \) in the liquid curve [22]; please see the two parallel dotted lines in Fig. 1.

  2. The driving free energy for each dissipation process cannot be self-derived by the MEPP for the nonlinear thermodynamics and needs to be prescribed by the TEP or the molar Gibbs energy diagram [34].

  3. The Gibbs free energy as a function of the concentration follows the parabola function.

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Acknowledgements

Haifeng Wang would like to thank the support of Alexander von Humboldt Foundation for a research fellowship. Haifeng Wang and Feng Liu are grateful to the National Basic Research Program of China (973 Program, No. 2011CB610403), the National Science Funds for Distinguished Young Scientists (No. 51125002), the Natural Science Foundation of China (Nos. 51371149, 51101122 and 51071127), the NSFC-RFBR Collaboration Project (No. 512111059), the Aeronautical Science Foundation of China (No. 2011ZF53067), and the 111 Project (No. B08040) of Northwestern Polytechnical University. Financial support by Deutsche Forschungsgemeinschaft within the contract HE1601/26 is gratefully acknowledged by D.M. Herlach.

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Authors and Affiliations

  1. State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, **’an, 710072, Shaanxi, People’s Republic of China

    Haifeng Wang & Feng Liu

  2. Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170, Cologne, Germany

    Haifeng Wang & D. M. Herlach

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  1. Haifeng Wang
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Correspondence to Haifeng Wang.

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Wang, H., Liu, F. & Herlach, D.M. Modeling the growth kinetics of a multi-component stoichiometric compound. J Mater Sci 49, 1537–1543 (2014). https://doi.org/10.1007/s10853-013-7835-2

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